x2+16x/2=36

Solution for x2+16x/2=36 equation:

x2+16x/2=36

We move all terms to the left:

x2+16x/2-(36)=0

We add all the numbers together, and all the variables

x^2+16x/2-36=0

We multiply all the terms by the denominator


x^2*2+16x-36*2=0

We add all the numbers together, and all the variables

x^2*2+16x-72=0

Wy multiply elements

2x^2+16x-72=0

a = 2; b = 16; c = -72;
Δ = b2-4ac
Δ = 162-4·2·(-72)
Δ = 832
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8\sqrt{13}}{2*2}=\frac{-16-8\sqrt{13}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8\sqrt{13}}{2*2}=\frac{-16+8\sqrt{13}}{4}
$